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- Title
Optimal Shape Factor and Fictitious Radius in the MQ-RBF: Solving Ill-Posed Laplacian Problems.
- Authors
Chein-Shan Liu; Chung-Lun Kuo; Chih-Wen Chang
- Abstract
To solve the Laplacian problems, we adopt a meshless method with the multiquadric radial basis function (MQRBF) as a basis whose center is distributed inside a circle with a fictitious radius. A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function. A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function. We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm. The novel method provides the optimal values of parameters and, hence, an optimal MQ-RBF; the performance of the method is validated in numerical examples. Moreover, nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition; this can overcome the problem of these problems being ill-posed. The optimal MQ-RBF is extremely accurate. We further propose a novel optimal polynomial method to solve the nonharmonic problems, which achieves high precision up to an order of 10-11.
- Subjects
RADIAL basis functions; GOLDEN ratio; POISSON'S equation; SEARCH algorithms; POLYNOMIAL time algorithms
- Publication
CMES-Computer Modeling in Engineering & Sciences, 2024, Vol 139, Issue 3, p3189
- ISSN
1526-1492
- Publication type
Article
- DOI
10.32604/cmes.2023.046002